The Unital Ext-Groups and Classification of C*-Algebras

Jamie Gabe, RUIZ EFREN

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Abstract

The semigroups of unital extensions of separable C∗-algebras come in two flavours: a strong and a weak version. By the unital Ext-groups, we mean the groups of invertible elements in these semigroups. We use the unital Ext-groups to obtain K-theoretic classification of both unital and non-unital extensions of C∗-algebras, and in particular we obtain a complete K-theoretic classification of full extensions of UCT Kirchberg algebras by stable AF algebras.

Original languageEnglish
JournalGlasgow Mathematical Journal
Volume62
Issue number1
Pages (from-to)201-231
ISSN0017-0895
DOIs
Publication statusPublished - Jan 2020

Keywords

  • 2010 Mathematics Subject Classification 46L3546L80

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